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Lecture
Functor Hom: Abelian Groups
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Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
Adjoints of Restriction Functor
Covers the adjoints of the restriction functor in group theory.
Functors and Homomorphisms in Group Theory
Explores functors F_{Ab} and Hom (-,-) in group theory, including presentations and homomorphisms.
Exact Sequences: Torsion and Divisibility
Explores exact sequences of abelian group homomorphisms and provides examples.
Natural Transformations: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Morphism of Groups
Covers the concept of morphism of groups, actions on sets, and automorphisms.
Restriction Functors: Group Actions
Introduces the concept of restriction functors in group actions.
Quotients in Abelian Groups
Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.
Torsion: Hom Functoriality and Exact Sequences
Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.
Group Theory - Part 2
Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.
